The PHAROS spectrometer at LANSCE is beginning to make important contributions to the LANL effort in Science Based Stockpile Stewardship. In the next LANSCE operating cycle, it is expected that a number of important measurements on 242Pu will be performed with PHAROS. The excellent energy resolution of the PHAROS spectrometer makes it an ideal instrument for measuring the phonon densities of states and neutron Brillouin scattering from 242Pu at ambient temperature and pressure. It is also expected that PHAROS will be an excellent instrument for measuring dispersion curves from d-242Pu once a single crystal is available. As described here, however, there are a number of important experiments for which the HELIOS spectrometer would be much more suitable than PHAROS, and HELIOS should enable new experimental investigations.
Most importantly, the HELIOS spectrometer will make possible experiments on Pu under pressure. The difficulty with neutron inelastic scattering experiments with samples under pressure is the scattering from the pressure cell. Scattering from the pressure cell can readily overwhelm the scattering from a small sample of a specialty isotope. The HELIOS design, with its high intensity and oscillating radial collimators, will be ideal for measurements on small samples in a pressure cell. If HELIOS construction starts within a year, the pressure experiments on HELIOS should match well the timetable for the completion of a number of important experiments on 242Pu with the PHAROS spectrometer. Although such work is classified, we present here some ideas for experiments on HELIOS, and we suggest these experiments are relevant to the SBSS mission.
Over the past year there has developed a collaboration between Fultz at Caltech and Drs. Rob Robinson and George Kwei at Los Alamos. Together with a bright LANL postdoctoral fellow, Rob McQueeney, this group has already undertaken several productive collaborations on studies of phonons in metals using inelastic neutron scattering. We hope this ongoing interaction between university and LANL personnel will move forward into experiments of high relevance to the SBSS effort.
Quite independently, Kwei and Fultz recognized that the difficulty of performing experiments on plutonium would require practice with an analog material. Both concluded that cerium metal is the obvious choice. Cerium assumes four crystal structures at atmospheric pressure, and some transformations between these phases are related to electronic instabilities of its valence electrons. In this respect, cerium has similarities to plutonium metal, but is much easier to study. Experimental techniques for making measurements at different temperatures and pressures are now being refined through work on cerium metal, and these methods should later be applicable to studies on plutonium metal.
The first experiment resulted in a manuscript submitted to Phys. Rev. Lett. [A]. It reports inelastic neutron scattering mea-surements on Ce metal at temperatures near the fcc (g) to bcc (d) transition, and presents approximate phonon DOS curves. A large difference in the phonon DOS of the g-Ce and d-Ce was found, providing a change in vibrational entropy at the g-d transition temperature of (0.51+-0.05) kB/atom. To be consistent with the latent heat of the g-d transition, this large change in vibrational entropy must be accompanied by a thermodynamically-significant change in electronic entropy of the opposite sign. This is the first evidence for a large electronic entropy contribution to the g-d phase transition. It is an exciting result, since it is the first case of a high-temperature structural phase transition in a material where electronic entropy is important. We expect that electronic entropy will play a similar role in the stability of the different solid phases of Pu metal.
Two more experiments on Ce were performed with the LRMECS spectrometer at IPNS at the Argonne National Lab. Data analysis for these measurements on Ce at low and high temperatures is still underway. It is expected that the anharmonicity of the phonons in fcc g-Ce will be determined. The heat capacity of g-Ce has been measured at elevated temperatures, and it is considerably higher than the classical limit for a harmonic solid. Some of this excess heat capacity can be associated with the softening of the phonon DOS, but we also expect a contribution from the temperature-dependence of the electronic entropy in g-Ce. Without electronic entropy, it can be shown that:
9 Bv a^2 T = Cp(T) - CV(T) = -T [dSvib/dT] ,
where dSvib is defined as the change in vibrational entropy caused by the change in phonon DOS over the temperature range dT. While the first equality is rigorous (we derive this equality to impress students of thermodynamics with the power of the Maxwell relations), the second equality is true only if the electronic entropy is negligible. We are testing this relationship with the temperature dependence of the phonon DOS of g-Ce. The same sort of experiments on d- and d'-Pu should be even more interesting, since their negative thermal expansion indicates that their anharmonicity is even larger. A temperature-dependence of the electronic entropy is a possible reason why phases in plutonium metal undergo negative thermal expansion.
In a preliminary experiment during our last beamtime allocation at LRMECS, we measured the phonon DOS of the shape memory alloy Ni-Ti [B]. Data analysis is nearly complete, and some results are clear. There is a substantial difference between the phonon DOS of the high temperature "austenite" and low temperature "martensite" phases of NiTi. This difference is approximately consistent with the latent heat of the transformation measured by calorimetry. More specifically, it appears that most of this difference in vibrational entropy is caused by changes in low energy phonons. It is interesting that low energy phonons have also been associated with the displacive mechanism of the phase transformation in Ni-Ti [C].
The phonon DOS of anharmonic solids will usually stiffen under pressure, leading to a reduced entropy, for example. Another important consequence is an increase in the velocities of sound. At high pressures the increased speed of sound makes it possible to generate a shock wavefront that propagates through the material. Measuring the pressure dependence of phonon dispersion curves of a metal is an excellent way to understand the pressure conditions required for shock wave generation.
An unusual phenomena should occur when driving high pressure waves through a material with negative coefficient of thermal expansion such as d-Pu. Negative thermal expansion indicates a negative Grneisen constant, meaning that the phonon DOS of d-Pu softens with increasing pressure. This would tend to suppress shock wave formation. However, it is not obvious that all phonon modes will have negative mode Grneisen constants. For example, the phonon softening in Co3V at elevated temperature is predicted very poorly with an average Grneisen constant [D].
Studies on single crystals under pressure would provide the most useful data. Nevertheless, it should be possible to obtain some of this information with a mix of neutron Brillouin scattering and phonon DOS measurements. With the configuration of the PHAROS I spectrometer, Fultz, Robinson, and Kwei will soon attempt to measure an average dispersion of longitudinal waves from polycrystalline Ce metal. These neutron Brillouin scattering experiments can provide crystallographically-averaged cuts through the dispersion surface of long wavelength phonons. Changes with temperature of the average intensities in the constant- energy cuts from these data, for example, should reveal the temperature-dependence of the average speed of longitudinal soundwaves. The shapes of these measured intensity dispersions should provide the distribution of sound velocities along different crystallographic directions.
Beam collimation to suppress scattering from a pressure cell is difficult in forward geometry, however, so experiments with the sample under pressure cannot be performed so readily. Although these measurements will be attempted on PHAROS, it is likely that Brillouin scattering experiments will not be possible with the sample under pressure. It is most practical to characterize thoroughly the phonon DOS of Ce and 242Pu with the PHAROS spectrometer with the sample at various temperatures. Pressure-dependent experiments are less appropriate for PHAROS.
The HELIOS spectrometer would be the ideal instrument for experiments on metals under pressure, owing to its higher intensity and its oscillating radial collimators. It is expected that by the time the HELIOS spectrometer is completed, the features of the phonon DOS of Ce and 242Pu will be adequately understood so that it will be known which features of the phonon DOS correspond to which phonon polarizations. (Unfortunately, neutron Brillouin scattering experiments will not be possible with HELIOS, owing to its limited energy resolution.)
Plutonium metal should exhibit a rich set of phase transitions at relatively modest pressures. We do not have access to classified literature on this subject, so the following comments must be considered speculative. Thermodynamically, however, the large specific volume of fcc d-Pu must make it quite unstable against pressure-driven transformations (to a- Pu, perhaps), and these should occur at pressures of several kbar. If the latent heat of these transformations have been measured under pressure, we should be able to determine independently the pressure dependencies of the electronic and phonon entropies. Furthermore, phonon softening may be a precursor to some of the low-temperature transformations in plutonium metal, which likely occur by diffusionless processes. Interpretations of the thermodynamics and kinetics of these transformations would proceed along the lines we are following for the work on NiTi [B].
The PHAROS weapons research effort will benefit from the development of HELIOS. An important part of the work on Pu will be the measurement of phonon dispersion curves from single crystals. This work will require a significant effort to develop experimental techniques and software for the analysis of phonon dispersion curves with a time-of-flight instrument. Software for this work will be developed in the software effort proposed for the HELIOS spectrometer. A larger user program and a higher level of scientific activity associated with the presence of HELIOS will help the development of experimental methods needed for single crystal work with PHAROS.
Some experimental problems will benefit from the use of both PHAROS and HELIOS. Measurements of phonon dispersion curves from small single crystals of 242Pu are expected to be limited by neutron flux. The most appropriate way to perform these experiments is to start by making several precise measurements on PHAROS. The excellent energy resolution of the PHAROS spectrometer will facilitate the identification of the phonon dispersion curves. For measurements at many different crystal orientations or at different pressures and temperatures, however, it would be most appropriate to use an instrument such as HELIOS, which offers much stronger signals. The flexibility of having the HELIOS instrument to complement PHAROS will facilitate all inelastic scattering research at LANSCE, including the weapons efforts.
A. J. L. Robertson, H. N. Frase, B. Fultz and R. McQueeney,"Phonon densities of states of g-Ce and d-Ce measured by inelastic neutron scattering", submitted to Phys Rev. Lett.
B. P. D. Bogdanoff, B. Fultz, J. L. Robertson, R. McQueeney, S. Rosenkranz, "Phonon Density of States and Heat Capacity of the Austenite-Martensite Transformation in the Shape Memory Alloy NiTi", manuscript in preparation.
C. S. K. Satuja, S. M. Shapiro, M. B. Salamon, and C. M. Wayman, "Phonon Softening in Ni46.8Ti50Fe3.2", Phys. Rev. B 29, 6031 (1984). H. Chou and S. M. Shapiro, "Observation of predicted phonon anomalies in b-phase Ni50Al50", Phys. Rev. B 48, 16088 (1993).
D. L. J. Nagel, B. Fultz, and J. L. Robertson, "Vibrational Entropies of Phases of Co3V Measured by Inelastic Neutron Scattering and Cryogenic Calorimetry", Philos. Mag. B 75 (1997) p. 681-699.